Solution:

To solve the given differential equation, we will use the method of separation of variables. The equation is given as:

dy/dt = 4y

Separating variables:
To separate the variables, we will move all terms involving y to one side and all terms involving t to the other side.

1/y dy = 4 dt

Integrating both sides:
Next, we will integrate both sides of the equation with respect to their respective variables.

∫(1/y) dy = ∫4 dt

Integral of (1/y) dy:
The integral of (1/y) dy can be evaluated as ln|y| + C1, where C1 is the constant of integration.

Integral of 4 dt:
The integral of 4 dt is simply 4t + C2, where C2 is the constant of integration.

Combining the results:
Now we can combine the results of the integrals:

ln|y| + C1 = 4t + C2

Combining constants:
We can combine the constants of integration into a single constant. Let's call it C.

ln|y| = 4t + C

Exponentiating both sides:
To eliminate the natural logarithm, we will exponentiate both sides of the equation. This will give us:

|y| = e^(4t + C)

Removing absolute value:
Since the exponential function is always positive, we can remove the absolute value signs. This gives us two possibilities:

y = e^(4t + C) or y = -e^(4t + C)

Applying initial condition:
To determine the specific solution, we need to apply the initial condition y(0) = 0.

For y = e^(4t + C):
y(0) = e^(4(0) + C) = e^C

Since y(0) = 0, e^C must be equal to 0. However, the exponential function is never equal to 0. Therefore, this possibility does not satisfy the initial condition.

For y = -e^(4t + C):
y(0) = -e^(4(0) + C) = -e^C

Since y(0) = 0, -e^C must be equal to 0. This is only possible if e^C = 0, which is not true. Therefore, this possibility also does not satisfy the initial condition.

Conclusion:
The given initial condition y(0) = 0 does not have a solution for the given differential equation dy/dt = 4y.